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Improving tatonnement methods for solving heterogenous agent models

Author

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  • Alexander Ludwig
Abstract
This paper develops a globally convergent algorithm which modifies standard block Gauss-Seidel iterations used by tatonnement methods for solving large scale deterministic heterogenous agent models. It is shown that the restrictions on the structure of the Jacobi matrix implicit in any such first-order iterative method can easily be relaxed for these models. Instead of relying on {\it ad hoc} and fixed dampening factors, standard Quasi-Newton methods can be used to determine the exact Jacobi matrix for steady state calculations and to update its elements by Broyden's method as the iteration proceeds. By transforming variables such that they are constant in the steady states, very few elements of the Jacobian have to be determined. For transition calculations the resulting steady state Jacobi matrix can be used as an approximation of the true transition Jacobi matrix. This extension of standard Gauss-Seidel iterations is shown to considerably improve convergence both in terms of speed as well as robustness relative to an ad hoc choice of fixed dampening factors. In addition, the relative advantage of the modified algorithm increases in the number of state variables of the model. The algorithm is particularly attractive since it is easy to implement - it only augments conventional and intuitive tatonnement iterations by standard numerical methods

Suggested Citation

  • Alexander Ludwig, 2004. "Improving tatonnement methods for solving heterogenous agent models," 2004 Meeting Papers 498, Society for Economic Dynamics.
    • Handle: RePEc:red:sed004:498
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    References listed on IDEAS

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    1. Axel Börsch‐Supan & Alexander Ludwig & Joachim Winter, 2006. "Ageing, Pension Reform and Capital Flows: A Multi‐Country Simulation Model," Economica, London School of Economics and Political Science, vol. 73(292), pages 625-658, November.
    2. David Domeij & Martin Flodén, 2006. "Population Aging And International Capital Flows," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 1013-1032, August.
    3. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    4. Juillard, Michel, 1996. "Dynare : a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm," CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP.
    5. Judd, Kenneth L., 2002. "The parametric path method: an alternative to Fair-Taylor and L-B-J for solving perfect foresight models," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1557-1583, August.
    6. Juillard, Michel & Laxton, Douglas & McAdam, Peter & Pioro, Hope, 1998. "An algorithm competition: First-order iterations versus Newton-based techniques," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1291-1318, August.
    7. David Altig, 2001. "Simulating Fundamental Tax Reform in the United States," American Economic Review, American Economic Association, vol. 91(3), pages 574-595, June.
    8. repec:adr:anecst:y:1990:i:17:p:04 is not listed on IDEAS
    9. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
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    Cited by:

    1. Axel Börsch‐Supan & Alexander Ludwig & Joachim Winter, 2006. "Ageing, Pension Reform and Capital Flows: A Multi‐Country Simulation Model," Economica, London School of Economics and Political Science, vol. 73(292), pages 625-658, November.
    2. Axel Börsch-Supan & Alexander Ludwig, 2010. "Old Europe Ages: Reforms and Reform Backlashes," NBER Chapters, in: Demography and the Economy, pages 169-204, National Bureau of Economic Research, Inc.
    3. Alexander Ludwig, 2005. "Moment estimation in Auerbach-Kotlikoff models: How well do they match the data?," MEA discussion paper series 05093, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    4. Axel Börsch-Supan & Alexander Ludwig & Joachim Winter, 2006. "Ageing, Pension Reform and Capital Flows: A Multi-Country Simulation Model," Economica, London School of Economics and Political Science, vol. 73(292), pages 625-658, November.
    5. Alexander Ludwig, 2005. "Aging and Economic Growth: The Role of Factor Markets and of Fundamental Pension Reforms," MEA discussion paper series 05094, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.

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    More about this item

    Keywords

    OLG models; Gauss-Seidel iterations;

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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